Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | #322×D73 |
| Fitting | #322×C73 ⋊ C2 |
| Sylow | C73 ⋊ C2×#322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D73 |
| commutator | C2×C73 | C2×C4×C8 |
| Fitting | #322×C73 | C2 |
| socle | C22×C73 | C2×C42 |
| hypercenter | #322 | D73 |
| hypocenter | C73 | C2×#322 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C42 ◁ #322 | |
248 conjugacy classes of subgroups.
1520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1313×D73, #32994983, #32995035, … |
| maximal normal subgroup of | #1313×D73, #32994983, #32995035, … |
| maximal quotient of | #322×Dic73, #1273×D73, #32976406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 2784);